Fuzzy set theory and its applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston <<[u.a.]>>
Kluwer Acad. Publ.
1994
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| Edition: | 2., rev. ed., 7. print. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 399 S. graph. Darst. |
| ISBN: | 079239075X |
Staff View
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Record in the Search Index
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| adam_text | Titel: Fuzzy set theory - and its applications
Autor: Zimmermann, Hans-Jürgen
Jahr: 1994
Contents List of Figures ix List of Tables xiii Foreword XV Preface xvii Preface for the Revised Edition xix 1 Introduction to Fuzzy Sets 1 1.1 Crispness, Vagueness, Fuzziness, Uncertainty 1 1.2 Fuzzy Set Theory 5 Part One: Fuzzy Mathematics 9 2 Fuzzy Sets—Basic Definitions 11 2.1 Basic Definitions 11 2.2 Basic Set-Theoretic Operations for Fuzzy Sets 16 3 Extensions 23 3.1 Types of Fuzzy Sets 23 3.2 Further Operations on Fuzzy Sets 28 3.2.1 Algebraic Operations 28 3.2.2 Set-Theoretic Operations 29 3.2.3 Criteria for Selecting Appropriate Aggregation Operators 39 4 Fuzzy Measures and Measures of Fuzziness 45 4.1 Fuzzy Measures 45 4.2 Measures of Fuzziness 47 5 The Extension Principle and Applications 53 5.1 The Extension Principle 53 5.2 Operations for Type 2 Fuzzy Sets 55 5.3 Algebraic Operations with Fuzzy Numbers 57 V
VI CONTENTS 5.3.1 Special Extended Operations 59 5.3.2 Extended Operations for /.^-Representation of Fuzzy Sets 62 6 Fuzzy Relations and Fuzzy Graphs 69 6.1 Fuzzy Relations on Sets and Fuzzy Sets 69 6.1.1 Compositions of Fuzzy Relations 74 6.1.2 Properties of the Min-Max Composition 77 6.2 Fuzzy Graphs 82 6.3 Special Fuzzy Relations 85 7 Fuzzy Analysis 91 7.1 Fuzzy Functions on Fuzzy Sets 91 7.2 Extrema of Fuzzy Functions 93 7.3 Integration of Fuzzy Functions 98 7.3.1 Integration of a Fuzzy Function over a Crisp Interval 98 7.3.2 Integration of a (Crisp) Real-Valued Function over a Fuzzy Interval 101 7.4 Fuzzy Differentiation 105 8 Possibility Theory, Probability Theory, and Fuzzy Set Theory 109 8.1 Possibility Theory 110 8.1.1 Fuzzy Sets and Possibility Distributions 110 8.1.2 Possibility and Necessity Measures 114 8.2 Probability of Fuzzy Events 117 8.2.1 Probability of a Fuzzy Event as a Scalar 118 8.2.2 Probability of a Fuzzy Event as a Fuzzy Set 119 8.3 Possibility vs. Probability 121 Part Two: Applications of Fuzzy Set Theory 129 9 Fuzzy Logic and Approximate Reasoning 131 9.1 Linguistic Variables 131 9.2 Fuzzy Logic 139 9.2.1 Classical Logics Revisited 139 9.2.2 Truth Tables and Linguistic Approximation 143 9.3 Approximate Reasoning 146 9.4 Fuzzy Languages 148 9.5 Support Logic Programming 157 9.5.1 Support Horn Clause Logic Representation 158 9.5.2 Approximate Reasoning in SLOP 162 10 Expert Systems and Fuzzy Control 171 10.1 Fuzzy Sets and Expert Systems 171 10.1.1 Introduction to Expert Systems 171 10.1.2 Uncertainty Modeling in Expert Systems 179 10.1.3 Applications 182 10.2 Fuzzy Control 201
vii 201 202 209 217 217 219 219 219 220 220 220 236 241 241 248 250 254 261 265 265 272 283 283 285 286 290 293 294 296 299 307 313 314 321 327 333 333 337 339 344 345 346 Introduction to Fuzzy Control Process of Fuzzy Control Applications of Fuzzy Control Pattern Recognition Models for Pattern Recognition The Data Structure or Pattern Space Feature Space and Feature Selection Classification and Classification Space Fuzzy Clustering Clustering Methods Cluster Validity Decision Making in Fuzzy Environments Fuzzy Decisions Fuzzy Linear Programming Symmetric Fufczy LP Fuzzy LP with Crisp Objective Function Fuzzy Dynamic Programming Fuzzy Multi Criteria Analysis Multi Objective Decision Making Multi Attributive Decision Making Fuzzy Set Models in Operations Research Introduction Fuzzy Set Models in Logistics Fuzzy Approach to the Transportation Problem Fuzzy Linear Programming in Logistics Fuzzy Set Models in Production Control and Scheduling A Fuzzy Set Decision Model as Optimization Criterion Job-Shop Scheduling with Expert Systems A Method to Control Flexible Manufacturing Systems Aggregate Production and Inventory Planning Fuzzy Mathematical Programming for Maintenance Scheduling Scheduling Courses, Instructors, and Classrooms Fuzzy Set Models in Inventory Control A Discrete Location Model Empirical Research in Fuzzy Set Theory Formal Theories vs. Factual Theories vs. Decision Technologies Models in Operations Research and Management Science Testing Factual Models Empirical Research on Membership Functions Type A-Membership Model Type B-Membership Model
CONTENTS VÜi 14.3 Empirical Research on Aggregators 355 14.4 Conclusions 367 15 Future Perspectives 369 Bibliography 373 Index 393
|
| adam_txt |
Titel: Fuzzy set theory - and its applications
Autor: Zimmermann, Hans-Jürgen
Jahr: 1994
Contents List of Figures ix List of Tables xiii Foreword XV Preface xvii Preface for the Revised Edition xix 1 Introduction to Fuzzy Sets 1 1.1 Crispness, Vagueness, Fuzziness, Uncertainty 1 1.2 Fuzzy Set Theory 5 Part One: Fuzzy Mathematics 9 2 Fuzzy Sets—Basic Definitions 11 2.1 Basic Definitions 11 2.2 Basic Set-Theoretic Operations for Fuzzy Sets 16 3 Extensions 23 3.1 Types of Fuzzy Sets 23 3.2 Further Operations on Fuzzy Sets 28 3.2.1 Algebraic Operations 28 3.2.2 Set-Theoretic Operations 29 3.2.3 Criteria for Selecting Appropriate Aggregation Operators 39 4 Fuzzy Measures and Measures of Fuzziness 45 4.1 Fuzzy Measures 45 4.2 Measures of Fuzziness 47 5 The Extension Principle and Applications 53 5.1 The Extension Principle 53 5.2 Operations for Type 2 Fuzzy Sets 55 5.3 Algebraic Operations with Fuzzy Numbers 57 V
VI CONTENTS 5.3.1 Special Extended Operations 59 5.3.2 Extended Operations for /.^-Representation of Fuzzy Sets 62 6 Fuzzy Relations and Fuzzy Graphs 69 6.1 Fuzzy Relations on Sets and Fuzzy Sets 69 6.1.1 Compositions of Fuzzy Relations 74 6.1.2 Properties of the Min-Max Composition 77 6.2 Fuzzy Graphs 82 6.3 Special Fuzzy Relations 85 7 Fuzzy Analysis 91 7.1 Fuzzy Functions on Fuzzy Sets 91 7.2 Extrema of Fuzzy Functions 93 7.3 Integration of Fuzzy Functions 98 7.3.1 Integration of a Fuzzy Function over a Crisp Interval 98 7.3.2 Integration of a (Crisp) Real-Valued Function over a Fuzzy Interval 101 7.4 Fuzzy Differentiation 105 8 Possibility Theory, Probability Theory, and Fuzzy Set Theory 109 8.1 Possibility Theory 110 8.1.1 Fuzzy Sets and Possibility Distributions 110 8.1.2 Possibility and Necessity Measures 114 8.2 Probability of Fuzzy Events 117 8.2.1 Probability of a Fuzzy Event as a Scalar 118 8.2.2 Probability of a Fuzzy Event as a Fuzzy Set 119 8.3 Possibility vs. Probability 121 Part Two: Applications of Fuzzy Set Theory 129 9 Fuzzy Logic and Approximate Reasoning 131 9.1 Linguistic Variables 131 9.2 Fuzzy Logic 139 9.2.1 Classical Logics Revisited 139 9.2.2 Truth Tables and Linguistic Approximation 143 9.3 Approximate Reasoning 146 9.4 Fuzzy Languages 148 9.5 Support Logic Programming 157 9.5.1 Support Horn Clause Logic Representation 158 9.5.2 Approximate Reasoning in SLOP 162 10 Expert Systems and Fuzzy Control 171 10.1 Fuzzy Sets and Expert Systems 171 10.1.1 Introduction to Expert Systems 171 10.1.2 Uncertainty Modeling in Expert Systems 179 10.1.3 Applications 182 10.2 Fuzzy Control 201
vii 201 202 209 217 217 219 219 219 220 220 220 236 241 241 248 250 254 261 265 265 272 283 283 285 286 290 293 294 296 299 307 313 314 321 327 333 333 337 339 344 345 346 Introduction to Fuzzy Control Process of Fuzzy Control Applications of Fuzzy Control Pattern Recognition Models for Pattern Recognition The Data Structure or Pattern Space Feature Space and Feature Selection Classification and Classification Space Fuzzy Clustering Clustering Methods Cluster Validity Decision Making in Fuzzy Environments Fuzzy Decisions Fuzzy Linear Programming Symmetric Fufczy LP Fuzzy LP with Crisp Objective Function Fuzzy Dynamic Programming Fuzzy Multi Criteria Analysis Multi Objective Decision Making Multi Attributive Decision Making Fuzzy Set Models in Operations Research Introduction Fuzzy Set Models in Logistics Fuzzy Approach to the Transportation Problem Fuzzy Linear Programming in Logistics Fuzzy Set Models in Production Control and Scheduling A Fuzzy Set Decision Model as Optimization Criterion Job-Shop Scheduling with Expert Systems A Method to Control Flexible Manufacturing Systems Aggregate Production and Inventory Planning Fuzzy Mathematical Programming for Maintenance Scheduling Scheduling Courses, Instructors, and Classrooms Fuzzy Set Models in Inventory Control A Discrete Location Model Empirical Research in Fuzzy Set Theory Formal Theories vs. Factual Theories vs. Decision Technologies Models in Operations Research and Management Science Testing Factual Models Empirical Research on Membership Functions Type A-Membership Model Type B-Membership Model
CONTENTS VÜi 14.3 Empirical Research on Aggregators 355 14.4 Conclusions 367 15 Future Perspectives 369 Bibliography 373 Index 393 |
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| spelling | Zimmermann, Hans-Jürgen Verfasser aut Fuzzy set theory and its applications H.-J. Zimmermann 2., rev. ed., 7. print. Boston <<[u.a.]>> Kluwer Acad. Publ. 1994 XX, 399 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Fuzzy sets Operations research Operations Research (DE-588)4043586-6 gnd rswk-swf Fuzzy-Menge (DE-588)4061868-7 gnd rswk-swf Operations Research (DE-588)4043586-6 s Fuzzy-Menge (DE-588)4061868-7 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016828948&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Zimmermann, Hans-Jürgen Fuzzy set theory and its applications Fuzzy sets Operations research Operations Research (DE-588)4043586-6 gnd Fuzzy-Menge (DE-588)4061868-7 gnd |
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| title | Fuzzy set theory and its applications |
| title_auth | Fuzzy set theory and its applications |
| title_exact_search | Fuzzy set theory and its applications |
| title_exact_search_txtP | Fuzzy set theory and its applications |
| title_full | Fuzzy set theory and its applications H.-J. Zimmermann |
| title_fullStr | Fuzzy set theory and its applications H.-J. Zimmermann |
| title_full_unstemmed | Fuzzy set theory and its applications H.-J. Zimmermann |
| title_short | Fuzzy set theory and its applications |
| title_sort | fuzzy set theory and its applications |
| topic | Fuzzy sets Operations research Operations Research (DE-588)4043586-6 gnd Fuzzy-Menge (DE-588)4061868-7 gnd |
| topic_facet | Fuzzy sets Operations research Operations Research Fuzzy-Menge |
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